Mathematical concepts can be represented in multiple ways. Teaching a concept together with the relationships between its multiple representations is regarded as one of the most important components of mathematics teaching. This study aims to examine the relationship between the ability to use geometric representation and algebraic representation bidirectionally on subject of conic sections. Sample of the study comprised 200 teacher candidates studying at Necmettin Erbakan University, Ahmet Keleşoğlu Education Faculty, Department of Mathematics Education. The questions were addressed to these mathematics teacher candidates at the end of the spring term 2016-2017, when they took the analytic geometry lesson. Quantitative research methods were used in the study. The problem sentence of this study is the success of bidirectional shift between the skill of ability of using algebraic representation and geometric representation on the subject of conic sections. In conclucion of the study, it was found that the mathematics teacher candidates were more successful in the geometrical representations than the algebraic representations and there was a meaningful difference in favor of in the geometrical representation of algebraic representations

Geometric representation • Algebraic representations • Conic section • Math teacher candidates

- Adu-Gyamfi, K. (1993). External multiple representations in mathematics teaching. (Master Thesis, North Carolina State University, USA) Retreived from http://www.lib.ncsu.edu/resolver/1840.16/366
- Arcavi, A. (2003). The role of visual representationsin the learning of mathematics. Educational Studies in Mathematics, 52, 215–241.
- Arslan, S. (2008). Diferansiyel denklemlerin öğretiminde farklı yaklaşimlar ve nitel yaklaşimın gerekliliği [Different approaches in the teaching of differential equations and the necessity of qualitative approach]. Milli Eğitim Dergisi [Journal of National Education], 179, 153-163.
- Aspinwall. L., & Shaw, K. L. (2002). Representations in calculus two contrasting cases. Mathematics Teacher, 95, 434-439.
- Baki, A. (2006). Kuramdan uygulamaya matematik eğitimi [Mathematics education from theory to practice]. Trabzon: Derya Bookstore.
- Boyer, C. B. (1968). A history of mathematics. Princeton, NJ: John Wiley & Sons.
- Brenner, M. E., Mayer, R. E., Moseley, B., Brar, T., Duran, R., Reed, B. S., & Webb, D. (1997). Learning by understanding: the role of multiple representations in learning algebra. American Educational Research Journal, 34(4), 663-689.
- Can, A. (2013). SPSS ile bilimsel araştırma sürecinde nicel veri analizi [Quantitative data analysis in the scientific research process with SPSS]. Ankara: Pegem Akademi.
- Delice, A., & Sevimli, E. (2010). Matematik öğretmeni adaylarının belirli integral konusunda kullanılan temsiller ile işlevsel ve kavramsal bilgi düzeyleri [Representations of mathematics teacher candidates used for specific integral and functional and conceptual knowledge level]. Gaziantep Üniversitesi Sosyal Bilimler Dergisi [Gaziantep University Journal of Social Sciences], 9(3). 581-605.
- Eroğlu, D., & Tanışlı, D. (2015). Elementary mathematics teachers’ knowledge of students and teaching strategies regarding the use of representations. Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi [Necatibey Education Faculty Electronic Science and Mathematics Education Journal], 9(1), 275-307.
- Gagatsis, A., & Elia, I. (2004). The effects of different modes of representation on mathematical problem solving. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, 2, 447–454.
- Gagatsis, A., & Shiakalli, M. (2004). Ability to translate from one representation of the concept of function to another and mathematical problem solving. Educational Psychology, 24(5), 645-657.
- Goerdt, L. S. (2007). The effect of emphasizing multiple representations on calculus students’ understanding of the derivative concept (Doctoral dissertation).Available from ProOuest Dissertations and Theses Database. (UMI No. 3277946).
- Goldin, G. A., & Kaput, J. (1996). A Joint perspective on the idea of representation. In L. P. Steffe, P. Nesher, G. A. Goldin, & B. Greer, (Eds.) Learning and doing mathematics, theories of mathematical learning, steffe (pp. 397-430). Mahwah, NJ: Erlbaum.
- Gözen, Ş. (2001). Matematik ve öğretimi [Mathematics and teaching]. İstanbul: Evrim Publishing.
- Hızarcı, S. (2004). Sunuş. In S. Hızarcı, A. Kaplan, A. S. İpek & C. Işık (Eds.), Euclid geometri ve özel öğretimi [Euclidean geometry and special teaching]. Ankara: Öğreti Publications.
- Keller, B. A., & Hirsch, C. R. (1998). Student preference for representations of functions. International Journal in Mathematics Education Science Technology, 29(1), 1-17.
- Milli Eğitim Bakanlığı [Ministry of Education], (2013). Ortaöğretim matematik dersi (9, 10, 11 ve 12.Sınıflar) öğretim programı [Secondary mathematics course (9th, 10th, 11th and 12th grade) curriculum]. Ankara.
- Mousoulides, N., & Gagatsis, A. (2004). Algebraic and geometric approach ın function problem solving. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, 3, 385–392.
- National Council of Teachers of Mathematics [NCTM] (2000). Principles and standards for school mathematics. Reston, VA: NCTM Publications.
- Neria, D., & Amit, M. (2004). Students preference of non-algebraic representations in mathematical communication'. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, 3, 409- 416.
- Oktaç, A. (2008). Ortaöğretim düzeyinde lineer cebir ile ilgili kavram yanılgıları [Misconceptions about linear algebra at secondary level]. In M. F. Özmantar, E. Bingölbali, & H. Akkoç (Eds.), Matematiksel kavram yanılgıları ve çözüm önerileri (s.121-150). [Mathematical concept misconceptions and solution proposal]. Ankara: Pegem Academy.
- Özhan Turan, A. (2011). 12.sınıf öğrencilerinin analitik geometrideki temsil geçişlerinin krutetskii düşünme yapıları bağlamında ı̇ncelenmesi; doğruların birbirine göre durumları [Examination of representative transitions of 12th grade students in analytical geometry in the context of krutetski thinking; situations according to each other]. (Master’s thesis, Marmara University, İstanbul, Turkey). Retrieved from https://tez.yok.gov.tr/UlusalTezMerkezi/
- Schultz, J. E., & Waters, M. S. (2000). Why representations?. Mathematics Teacher, 93(6), 448-453.
- Snowman, J., & Biehler, R. (2003). Psychology applied to teaching (10th ed.). Boston: Houghton Mifflin.
- Stewart, S., & Thomas, M. O. J. (2004). The learning of linear algebra concepts: Instrumentation of cas calculators. Proceedings of the 9th Asian Technology Conference in Mathematics, Singapore. 377-386.
- Topdemir, H. G. (2011). Apollonios ve Koni Kesitleri [Apollonius and Cone Sections]. Bilim ve Teknik. Ankara: Tübitak .

Year 2017,
Volume: 1 Issue: 1, 21 - 30, 01.12.2017
### Abstract

### References

- Adu-Gyamfi, K. (1993). External multiple representations in mathematics teaching. (Master Thesis, North Carolina State University, USA) Retreived from http://www.lib.ncsu.edu/resolver/1840.16/366
- Arcavi, A. (2003). The role of visual representationsin the learning of mathematics. Educational Studies in Mathematics, 52, 215–241.
- Arslan, S. (2008). Diferansiyel denklemlerin öğretiminde farklı yaklaşimlar ve nitel yaklaşimın gerekliliği [Different approaches in the teaching of differential equations and the necessity of qualitative approach]. Milli Eğitim Dergisi [Journal of National Education], 179, 153-163.
- Aspinwall. L., & Shaw, K. L. (2002). Representations in calculus two contrasting cases. Mathematics Teacher, 95, 434-439.
- Baki, A. (2006). Kuramdan uygulamaya matematik eğitimi [Mathematics education from theory to practice]. Trabzon: Derya Bookstore.
- Boyer, C. B. (1968). A history of mathematics. Princeton, NJ: John Wiley & Sons.
- Brenner, M. E., Mayer, R. E., Moseley, B., Brar, T., Duran, R., Reed, B. S., & Webb, D. (1997). Learning by understanding: the role of multiple representations in learning algebra. American Educational Research Journal, 34(4), 663-689.
- Can, A. (2013). SPSS ile bilimsel araştırma sürecinde nicel veri analizi [Quantitative data analysis in the scientific research process with SPSS]. Ankara: Pegem Akademi.
- Delice, A., & Sevimli, E. (2010). Matematik öğretmeni adaylarının belirli integral konusunda kullanılan temsiller ile işlevsel ve kavramsal bilgi düzeyleri [Representations of mathematics teacher candidates used for specific integral and functional and conceptual knowledge level]. Gaziantep Üniversitesi Sosyal Bilimler Dergisi [Gaziantep University Journal of Social Sciences], 9(3). 581-605.
- Eroğlu, D., & Tanışlı, D. (2015). Elementary mathematics teachers’ knowledge of students and teaching strategies regarding the use of representations. Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi [Necatibey Education Faculty Electronic Science and Mathematics Education Journal], 9(1), 275-307.
- Gagatsis, A., & Elia, I. (2004). The effects of different modes of representation on mathematical problem solving. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, 2, 447–454.
- Gagatsis, A., & Shiakalli, M. (2004). Ability to translate from one representation of the concept of function to another and mathematical problem solving. Educational Psychology, 24(5), 645-657.
- Goerdt, L. S. (2007). The effect of emphasizing multiple representations on calculus students’ understanding of the derivative concept (Doctoral dissertation).Available from ProOuest Dissertations and Theses Database. (UMI No. 3277946).
- Goldin, G. A., & Kaput, J. (1996). A Joint perspective on the idea of representation. In L. P. Steffe, P. Nesher, G. A. Goldin, & B. Greer, (Eds.) Learning and doing mathematics, theories of mathematical learning, steffe (pp. 397-430). Mahwah, NJ: Erlbaum.
- Gözen, Ş. (2001). Matematik ve öğretimi [Mathematics and teaching]. İstanbul: Evrim Publishing.
- Hızarcı, S. (2004). Sunuş. In S. Hızarcı, A. Kaplan, A. S. İpek & C. Işık (Eds.), Euclid geometri ve özel öğretimi [Euclidean geometry and special teaching]. Ankara: Öğreti Publications.
- Keller, B. A., & Hirsch, C. R. (1998). Student preference for representations of functions. International Journal in Mathematics Education Science Technology, 29(1), 1-17.
- Milli Eğitim Bakanlığı [Ministry of Education], (2013). Ortaöğretim matematik dersi (9, 10, 11 ve 12.Sınıflar) öğretim programı [Secondary mathematics course (9th, 10th, 11th and 12th grade) curriculum]. Ankara.
- Mousoulides, N., & Gagatsis, A. (2004). Algebraic and geometric approach ın function problem solving. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, 3, 385–392.
- National Council of Teachers of Mathematics [NCTM] (2000). Principles and standards for school mathematics. Reston, VA: NCTM Publications.
- Neria, D., & Amit, M. (2004). Students preference of non-algebraic representations in mathematical communication'. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, 3, 409- 416.
- Oktaç, A. (2008). Ortaöğretim düzeyinde lineer cebir ile ilgili kavram yanılgıları [Misconceptions about linear algebra at secondary level]. In M. F. Özmantar, E. Bingölbali, & H. Akkoç (Eds.), Matematiksel kavram yanılgıları ve çözüm önerileri (s.121-150). [Mathematical concept misconceptions and solution proposal]. Ankara: Pegem Academy.
- Özhan Turan, A. (2011). 12.sınıf öğrencilerinin analitik geometrideki temsil geçişlerinin krutetskii düşünme yapıları bağlamında ı̇ncelenmesi; doğruların birbirine göre durumları [Examination of representative transitions of 12th grade students in analytical geometry in the context of krutetski thinking; situations according to each other]. (Master’s thesis, Marmara University, İstanbul, Turkey). Retrieved from https://tez.yok.gov.tr/UlusalTezMerkezi/
- Schultz, J. E., & Waters, M. S. (2000). Why representations?. Mathematics Teacher, 93(6), 448-453.
- Snowman, J., & Biehler, R. (2003). Psychology applied to teaching (10th ed.). Boston: Houghton Mifflin.
- Stewart, S., & Thomas, M. O. J. (2004). The learning of linear algebra concepts: Instrumentation of cas calculators. Proceedings of the 9th Asian Technology Conference in Mathematics, Singapore. 377-386.
- Topdemir, H. G. (2011). Apollonios ve Koni Kesitleri [Apollonius and Cone Sections]. Bilim ve Teknik. Ankara: Tübitak .

There are 27 citations in total.

Other ID | JA85PR54VH |
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Journal Section | Research Article |

Authors | |

Publication Date | December 1, 2017 |

Published in Issue | Year 2017 Volume: 1 Issue: 1 |